Whether or not Project 2025 is a threat to US democracy depends on what you consider democracy to be.
If you believe in a living system where the Constitution and laws should be interpreted in a modern context (for whatever is 'modern' at the time) and informed by changes in scientific knowledge and societal norms, then it's a huge threat. If you believe in a strict adherence to the letter of the Constitution and law, regardless of the repercussions on 'modern' society, then it's simply restoring things to how they should be.
To provide a couple examples (mostly sourced from the links provided in the question):
- The first amendment states "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof...".
In a living interpretation, this means that any law which favors one
religion over another is unconstitutional. In a strict reading, a
law saying "Everyone must convert to <religion>" would be
unconstitutional, but one which pulls from that religion's values and
imposes them on everyone (follower or not) is fine.
- If you believe that modern scientific knowledge has become complex enough that no one can understand it all and laws/regulations should be imposed by a team of experts in the relevant field, then government agencies should be run by career civil servants who have deep knowledge of their sphere and have the power to effectively write the laws for it (subject to Congress's explicit instruction otherwise) and enforce the arcane details. If you believe that "[all] executive Power shall be vested in [the] President" and that "all legislative Powers ... shall be vested in a Congress", then there's no place for a bureaucracy to regulate anything not explicitly authorized by Congress.
- Constitutional amendments provide that "The right of citizens ... to vote shall not be denied or abridged ... on account of race, [or] color..." or sex or age.
If you believe in strictly adhering to these limits as specified, then any restrictions not based on those factors are fine. For instance, preventing citizens from voting due to lack of the correct paperwork or lack of access to the polling location is fine. If you believe in living interpretation, then laws that aren't specifically targeted at one of those factors are still prohibited if they have a disproportionate impact on people in one of those groups.
- The 14th amendment says that _"No State shall make or enforce any law which shall ... deny to any person within its jurisdiction the equal protection of the laws".
This can be read to mean that any law which promotes one group over another is prohibited, or it can be read to mean that there must be laws to make everyone equal. The first reading prohibits things such as affirmative action, because it favors minorities over the majority. The second reading requires affirmative action, to ensure that the minority is treated equally with the majority.
More fundamentally, Article II says that "The President shall be Commander in Chief of the Army", and the Insurrection Act allows the President to use the Army and National Guard to ensure that federal laws are enforced. Since it is physically impossible to enforce every law 100% of the time, it's then on the President to decide which laws are (in his/her interpretation) being broken to the extent that they need to be enforced by soldiers. In practical terms, that could mean anything from heavily armed guards at polling places checking every voters' ID to mass arrests and detentions is even suspected of being a terrorist, illegal immigrant, and/or protestor, or even outright opening fire on them. But since it's all done with the goal of making sure the laws are actually being upheld, then it's perfectly legal.
TL;DR
Project 2025 believes in adhering to the letter of the law, even if that violates the (presumed) spirit; that equality means no one is given any special treatment; and that using soldiers to enforce the President's interpretation of the laws is valid.
Opponents to it believe in adhering to the spirit of a law as seen through a modern lens, even if that goes way beyond the letter; that equality means bringing everyone up to the same level, even if that means assisting some more than others; and that the army should only be used against Americans in the most egregious of circumstances, leaving everything else to regular law enforcement agencies.
